{
  "aliases": [
    "parametric-surface"
  ],
  "backlinks": [
    {
      "field": "defines",
      "target": "05788J51WZ"
    },
    {
      "field": "uses",
      "target": "065HE5V98E"
    },
    {
      "field": "uses",
      "target": "073JKP99K2"
    },
    {
      "field": "uses",
      "target": "0S29Y4ZW0Y"
    }
  ],
  "body": "\n## Summary\n\nA parametrised surface is a surface in $\\mathbb{R}^3$ given by a map of two parameters into space.\nSurfaces in Stokes' theorem and the divergence theorem are often given in this form.\nFrom a parametrisation one can compute the surface area, the normal vectors and the curvature of the surface.\n",
  "commit": "6ac761d40018146541484a9e8b9eafd6ecc303dc",
  "front": {
    "aliases": [
      "parametric-surface"
    ],
    "kind": "concept",
    "msc": [
      "53A05"
    ],
    "name": "Parametrised surface",
    "same_as": {
      "wikidata": "Q1071743",
      "wikipedia": "Parametric surface"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Parametric_surface"
      }
    ],
    "tag": "0ZG9QF40HE"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/0ZG9QF40HE/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/0ZG9QF40HE.md",
  "msc": [
    "53A05"
  ],
  "name": "Parametrised surface",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0ZG/0ZG9QF40HE.md",
  "status": null,
  "tag": "0ZG9QF40HE",
  "uri": "m2://0ZG9QF40HE",
  "url": "https://math2.tamnd.com/wiki/parametrised-surface/",
  "writing": {
    "tag": "0ZG9QF40HE",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}